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I might be one of the rare few who has had luck with CLIs with Cap1. I started out with the plat on 6/11, with a $500 credit limit. However many statements later (it was two years ago, I forget how many statements the disclosure required), Cap1 bumped me to $750. A weekend ago, I notice that my CL had auto-increased to $2,250. After contacting EO, Cap1 was even nice enough to PC to Quicksilver.
Important things people will probably ask. My score was probably somewhere between 550–600 when I got the card; it's now just shy of 700. I probably paid late somewhere between once and three times, but not recently. I hadn't had any activity on the card for about two months when I got the CLI, and my income had skyrocketed. Hope this helps.
I have had good experiences with Cap 1. I got the platinum with a CL of 500 last october after a 4 year self imposed break from credit cards (prbly shouldnt have closed all the cards in hindsight...but oh well). They credit stepped me to 2000 in 6 months. I hit up the EO for a bump up to 4500 last month and a PC to QS1 (AF waived). So, I am pretty happy with them.